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Education and Innovation in Embedded Systems Design

USI Università della Svizzera italiana, USI Faculty of Informatics, Advanced Learning and Research Institute USI Università della Svizzera italiana USI Faculty of Informatics USI Advanced Learning and Research Institute
TitleBreaking ECC2K-130
Publication TypeJournal Article
Year of Publication2009
AuthorsBailey, D. V., L. Batina, D. J. Bernstein, P. Birkner, J. W. Bos, H. - Chung Chen, C. - Mou Cheng, G. van Damme, T. G├╝neysu, F. Gurkaynak, T. Kleinjung, C. Paar, F. Regazzoni, R. Niederhagen, P. Schwabe, L. Uhsadel, and A. Van Herrewege
JournalIACR Cryptology ePrint Archive
Date Published11/2009
KeywordsAttacks, automorphisms, binary fields, Certicom challenges, DLP, ECC, implementation, Koblitz curves, parallelized Pollard rho

Elliptic-curve cryptography is becoming the standard public-key primitive not only for mobile devices but also for high-security applications. Advantages are the higher cryptographic strength per bit in comparison with RSA and the higher speed in implementations. To improve understanding of the exact strength of the elliptic-curve discrete-logarithm problem, Certicom has published a series of challenges. This paper describes breaking the ECC2K-130 challenge using a parallelized version of Pollard's rho method. This is a major computation bringing together the contributions of several clusters of conventional computers, PlayStation~3 clusters, computers with powerful graphics cards and FPGAs. We also give /preseestimates for an ASIC design. In particular we present * our choice and analysis of the iteration function for the rho method; * our choice of finite field arithmetic and representation; * detailed descriptions of the implementations on a multitude of platforms: CPUs, Cells, GPUs, FPGAs, and ASICs; * details about running the attack.